RESEARCH ON MONITORING METHOD OF WORKING CONDITION FOR BEARING

RESEARCH ON MONITORING METHOD OF WORKING CONDITION FOR BEARING Ke HUANG *, Hongming ZHOU Mechanical and Electrical Engineering College of Wenzhou University, Wenzhou, 325035, China E-mail: hk125cn@163.com ABSTRACT: Aiming to the multi-feature detection of bearing vibration, the method of Dynamic Statistic principal component analysis was proposed. At first some dimensionless indexes which were sensitive to working condition of bearing were chosen as input variable for process monitoring model, and then the concept that zoom time signal was described in order to compute indexes above more corrective and divide data acquisition into many minizones, including calculation steps. At last taking motor bearing rotating at high speed and main bearing for shield machine at low speed as example, giving monitoring effect of each statistics respectively, such methods were proved effectively to monitor process state for bearing. KEY WORDS: bearing, principal component analysis, fault diagnosis, process monitoring. 1 INTRODUCTION At present, the vibration signal analysis method has been widely applied in the fault diagnosis of the mechanical equipment. Features of time domain, frequency domain and time-frequency domain which are extracted from vibration signals has also been widely used. For example, 15 statistics listed in literature (Widodo et al., 2009) lead to the difficulty of analysis due to the correlation of multiple features. The fault diagnosis of the bearing in the laboratory is mainly based on a single fault monitoring, while the actual situation is that the bearing failure is the result of the joint action of wear, damage or exfoliation. The difference lies in the various proportion of the failure state to the final result. For example, the failure of the main bearing in the shield machine is caused by the damage of seal. Specifically, the impurity enters the bearing, hence the wear of each movement pair is aggravated and the outer ring, roller and other parts are rusted. If the main bearing is not repaired in time, it is bound to replace it with a large bearing. The Principal Component Analysis (PCA) method summarizes features of original parameters by the variable transformation method of which the related variables is transformed into a few unrelated principal components. Hence, the fusion of multiple diagnostic parameters is realized (Liu, 2011). At present, some scholars have applied PCA to the fault diagnosis and analysis of rolling bearings, such as the literature (Fu et al., 2017; Gu et al., 2016; Fadda and Moussaoui, 2018). Besides, the PCA is improved due to the nonlinear and timevarying and other features of the bearing vibration signals. For example, the literature (Zhang et al., 2018; Mi and Hu, 2013; Xu et al., 2014) proposed the application of Kernel PCA analysis method on the fault diagnosis of bearings. The literature (Ou and Yu, 2014) selected the principal component analysis and supervised laplaian score (SLS) for bearing features, and then the classification of faults is realized. The literature (Wu et al., 2017) detected the characterization of the damage through normal bearing series obtained by the EMD and Hilbert transform analysis signals, Spielman grade (Spearman's rank) related parameters and PCA. The literature (Mohanty et al., 2017) analyzed the fault diagnosis by the average kurtosis technique which is based on EMD and PCA technology, and then good results are obtained. The literature (Li et al., 2008) applied KPCA (Kernel PCA, kernel principal component analysis) to the fault diagnosis of rolling bearings. The literature (Yan et al., 2005) proposed the application of KPCA in nonlinear systems. The literature (Zvokelj et al., 2010) proposed the multiscale PCA (MSPCA) method which is based on the ensemble empirical mode decomposition (EEMD). The multi-scale PCA (MSPCA) method takes conventional vibration signals and acoustic emission signals as input variables. The simulation results obtained through the EEMD-MSPCA method suggest that both two input signals above carry sufficient fault information and prove the reliability of this method in the bearing monitoring. Although the application of PCA obtained great success, the conventional fault diagnosis technology based on the PCA still has many shortcomings (Jeng, 2010). Most literature combines PCA with 128

other algorithms rather than essentially improving the PCA algorithm. The rolling bearings operation is a timevarying and dynamic process, hence the static PCA model is unable to effectively monitor the timevarying process and state. Therefore, it is necessary to update the adaptive state of the PCA model. In addition, there is a temporal correlation between the sample sequences when considering the short time interval of vibration data acquisition. To sum up, this paper proposes the dynamic statistic principal component analysis (Dynamic Statistic PCA, DSPCA) by combine advantages of mobile window PCA with the dynamic PCA. Besides, DSPCA is applied to the monitoring of rolling bearing operation. 2 IMPROVED PCA ALGORITHM This algorithm combines the basic principles of mobile window filtering with PCA. Basic steps are shown as follows. 1) Build a PCA model with the historical data, determine various statistic parameters, and standardize PCA. 2) Incorporate new data within the statistic control limit into the PCA model, delete the old data and update statistic parameters based on the new model. The literature proposed an adaptive mobile window algorithm of which the length of the mobile window adaptively changes with updating data. Liu et al., (2009) proposed a mobile window algorithm which is more effective and memory saving. However, neither the PCA model or updated algorithm in mobile window construction algorithm consider the correlation of the data sequence. In this paper, the dynamic PCA algorithm is combined with the mobile window algorithm, and formulas are updated. A complete moving window algorithm should consider the sample mean, the variance and covariance matrix that is recursively updated, the recursive algorithm to update the feature space and the confidence limit to update the monitoring indexes. It will be discussed in detail as follows. 2.1 Update covariance matrix The PCA model, mean vector, standard variance vector, standardize matrix and covariance matrix are constructed with historical data. Extend this matrix with consideration of the sequence correlation, hence the PCA model is matrix I. The initial statistic expressed by the block matrix is the mean vector, standard variance vector, standardize matrix and covariance matrix. The lower marker is a variable, the sample number at, and the time constant. The updated covariance matrix mainly consists of downdating and updating. STEP1: Delete in the matrix I ( is the row number of matrix I), and update all the statistic parameters. Hence, the new mean vector and standard deviation of each variable ( ) which are shown as follows are obtained. ( ) [ ] (1) (2) Where [( ) ( )] indicates the i th in each block, the i th in each block, the length of the mobile window,, the i th column of. The standard variance vector of matrix II is recorded as [ ]. Let the matrix I without be the matrix II, and the standardized matrix II (still uses the same symbol). ([ ] ([ ])) [ ] (3) Where,. The covariance matrix can be expressed as follows. ([ ]) ([ ]) ( ) ( )(4) Where. The covariance matrix II which is shown as follows of matrix is derived from the formula (1-4). 129

[ ] ( ) ( ) (5) STEP2: Add into the matrix II which then is regarded as matrix III, update and calculate each statistic. It is called Updating process. The mean and the variance of the matrix III are shown as follows. ( ) (6) ( ) ( ) (7) Where,,., 2.2 Update eigenvalue Assume the SVD (singular value decomposition) of the time covariance matrix at the moment as follows. (8) Where,.Let, Then (9) Let. (10) Because is the block matrix composed of diagonal matrices, its transposing does not affect the result. Similarly, let. Then (11) Combine (9), (10), (11) with (7). [ ] [ ] (12) Let (13) (14) Then [ ] [ ] (15) If [ ] meets the orthogonality, the eigenvalues can be updated to. is amatric composed of orthogonal arrays while [ ] is not an orthogonal array. In order to restore the orthogonality of the matrix, it is decomposed into two parts, and, by space projection. Put it another way, and are orthogonal and parallel to respectively. (16) In order to make the orthogonal to, the QR decompose should be carried out. (17) According to the (1-4) and (1-5), the results which is shown as follows is obtained. [ ] (18) (19) Collate all formulas above, the results which is shown as follows is obtained. (20) The result of the singular value decomposition of the middle term in (1-9) which is shown as follows is obtained. (21) Combine (1-20) and (1-21), the result which is shown as follows is obtained., (22) 2.3 Update monitoring statistics Since the PCA model of the system is updated, the statistics and its control limits also need to be updated adaptively. PCA divides the measurement space into the principal space and residual space. 130

Hence, the statistic and SPE (Squared Prediction Error or Q) describes the corresponding spatial changes respectively. At the moment, the PCA model is constructed by the matrix, and the number of principal components is obtained through its covariance matrix. Determine the number of principal components and measure the space. is the principal component space composed of eigenvectors corresponding to eigenvalues, and the latter is the residual space composed of residual vectors. The projection of the sample in the principal component space and residual space is divided into two parts, and. Where. is corresponding vectors ( ) of the principal component of. The sample is projected on the residual space, then SPE which is shown as follows is obtained. (23) (24) is shown as follows. Where. Similarly, two statistics of matrix III can be obtained. The formula for monitoring limit of statistics which can be referred to the relevant literature is not described in this paper. 3 CONSTRUCTION OF PRINCIPAL COMPONENT MODEL FOR VIBRATION SIGNAL 3.1 Input variables of principal component model Vibration signals of a bearing contain a wealth of bearing operating states which is easy to be obtaind, such as the fault state. Various statistics obtained from vibration signals by the statistic processing reflects various states of the bearing objectively. For example, the change of the mean square root in the abnormal vibration wave of the surface wear is small, hence the appropriate evaluation can be obtained. The peak value is sensitive to the component surface damage (Mei, 1996). In dimensionless index, the kurtosis index is the one most sensitive to the impact pulse caused by surface spalling(he et al., 2010). A simple diagnosis of the rolling bearing, whether the bearing is defective, can be realized through the static calculation of the vibration signals with these range parameters. In order to identify the state of the rolling bearing accurately, a variety of features are applied to comprehensively analyze the bearing. Due to the clear relationship of parameters, the interpretation ability of the model is strong. Considering the calculation steps of principal component analysis, this paper takes the main component analysis as input parameters of non dimensional index, and the formula of waveform index, peak index, pulse index, kurtosis index and margin index which are shown as follows[18] (a set of discrete data are, sampling interval is, sampling number is ). (25) (26) (27) (28) (29) Where is the root mean square, is the mean amplitude (absolute mean), is the maximum value in discrete signals, * + is the root amplitude, is the kurtosis. 3.2 Subdivision of time domain signal The usual sampling process is shown as follows. Firstly, preprocess the continuous signal. Then calculate the frequency of the signal, set the sampling frequency and sampling time (satisfy the shannon law) for the sampling and process the sampling value signal. Most signals in industry or engineering includes interference signals, such as noise. Besides, the number of discrete data effects the final result of the statistic, such as the analysis of positive and negative drift. When the positive matrix with the mean of 0.07 makes the initial matrix move 0.07 along the positive direction of the X axis, the negative matrix with mean of 0.06 makes the initial matrix move 0.06 along the negative direction of the X axis. The total mean is positive 0.01, hence the conclusion that the combination of the positive and negative drift is obtained. 131

The envelope analysis (upper envelope) takes peaks of vibration signals and connects each point with a curve to observe whether there is a pulse impact at a certain moment and at a certain frequency. Thus, whether a fault occurs can be judged. The envelope analysis and Fourier analysis take all the sampled values as a whole, rather than considering details. Hence, the results are "counted". On the contrary, if a interval with each peak as the center is formed, which is same with the subdivision of the vibration signal, and related signals is processed within each interval, the precision of the analysis can be improved. This process is called subdivision in this paper. The algorithm is shown as follows. Let the rotational speed of the rotating parts be, the rotation period be, the sampling frequency be, the sampling time be, the instantaneous amplitude i at the th sampling be. For,divide the sampling time according to the rotation period, which is same with divide of by. Thus, the sampling time is divided into J intervals, and the vibration sensors sampling times in each interval, which is. The kurtosis in each interval is calculated. The formulas are shown as follows. the amplitude of the kurtosis failing process. KV increases in the Figure 1. Time domain diagram for the subdivide kurtosis of normal bearing signals The subdivision helps to highlight the impact energy of the vibration and is more sensitive to impulse fault. Its application on the motor is shown as follows. Let the fault feature frequency of a bearing outer ring which can be obtained by the calculation of the bearing dimension be 159Hz, the fault feature frequency of the inner ring be 109Hz, the fault feature frequency of the cage be 70Hz, the frequency of the motor be 35Hz, the sampling frequency of the acceleration sensor be 12000 Hz. The setting of the spectrum resolution is shown as follows. Let the sampling period be 1/12000, the axis rotation Cycle be 1/35. According to the feature frequency of the cage fault, the axis turns one round, the cage turns 2 rounds, hence the sampling frequency 12000 contains 12000/70=171 complete feature frequency of the cage. Divide the sampled data into 171 blocks, calculate the kurtosis value or other statistics of each block, recombine the signal, and carry out the time domain analysis. The schematic diagram is shown in the Figure 1 and 2. The mean in the Figure 1 is 6.0513e-006 and that in the Figure 2 is 1.5706e-004, which suggests that 132 Figure 2. Time domain diagram for the subdivide kurtosis of failed bearing signals 4 EXPERIMENT 4.1 Experiment object In order to verify the feasibility of the method proposed in the first and second section, the study was carried out based on the data from the bearing data center of the Case Western Reserve University. Figure 3. Experiment for the rolling bearing

The bearings to be tested support the rotating shaft in the motor shown in fig.3. The code of the bearing on the drive end is SKF6205 and that of the Table 1. Geometry dimensions of bearings (inches) bearing on the fan end is SKF6203. Geometric dimensions of two kinds of bearings is listed in the Table 1. Code Diameter of inner ring Diameter of outer ring thickness Diameter of ball Pitch diameter 6203 0.6693 1.5748 0.4724 0.2656 1.122 6205 0.9843 2.0472 0.5906 0.3126 1.537 Take the dynamic principal component analysis into consideration. Let the time delay parameter be 2 and the input variables of the model to be constructed be. Let the motor speed be 1797, the bearing be SKF6203. Select four groups of samples which is normal bearing, bearing with failed ball, bearing with failed outer ring and bearing with failed inner ring. The so-called fault means a small pit with the diameter of 0.007mm is made on the ball, outer ring or inner ring. The model data and test data are obtained according to the subdivision method shown in the section 2.1. The result of process monitoring obtained from the MATLAB, the data processing platform, is shown as follows. In order to save space, only the diagram for the, SPE (or ) of the normal bearing and the bearing with failed outer are shown in the Figure 4 and Figure 5. The red line represents the control line of the confidence α=0.01, and the green line represents the control line of the confidence α=0.05. (1)T 2 of the normal bearing (2) Distribution of Q of the normal bearing (3) Contribution diagram of the normal bearing in the operation Figure 4. Monitoring of the normal bearing 133

(1) Outer ring fault (2) Outer ring fault Through the simulation test, it is found that both statistict 2 and Qcan achieve the monitoring of the normal bearing well. Contribution diagrams of each quantity are stable, the weight concentrates in the waveform index, the waveform index emphasizes the deviation and the distortion of its waveform when compared with the sinusoidal waveform. As for the failed bearing, the statistic T 2 and Qand its control limit achieve the monitoring for the fault of the ball, inner ring and outer ring. Besides, the contribution diagram involved in the 5 variables have obvious changes in weight. The weight not only explains the contribution of the variable to the current fault status, which is same with the change of weight compared to the Figure 4-3, but also indicates that all input variables of the principal component analysis are sensitive to the change of bearing operating state, which can be obtained from the distribution map and contribution diagram of statistic T 2 and Q. 4.2 Fault diagnosis based on the DSPCA for the main bearing of shield machine A certain type of MITSUBISHI earth pressure (3) Contribution diagram of the outer ring fault Figure 5. Monitoring of the outer ring fault balance shield machine 6340mm is applied. The power transmission line of the cutter disk drive system is the motor with the reducer, the main bearing, the tool disk body and the cutter head. The 8 sets of motors drive their small gears through the decelerator (deceleration gear), and then small gears drive external gear bearings that are glued to small gear. The rotation speed of the cutter disk generally lies between 0.77-1.55/min. The belt reducer of which code is MRP1743SC-630 and motor of which code MIE120/120-WLD2/4 is are all produced by the MITSUI MIIKE MACHINERY Co., Ltd. The rated power of the motor is 90KW, the pole is 4/8, the synchronous speed is 1500/750 (/min). The main bearing is a DTR2475TAGS-2 produced by the KOYO. The sensor is a low frequency acceleration sensor CMSS 797L produced by the SKF. The data acquisition unit is CMMA 7720-B produced by the SKF. The average rotational speed of spindle is 1.0r/min. The sampling frequency is 12KHz which is shown in the figure 6 and 7. 134

Figure 6. Test platform for the fault diagnosis of the main bearing Figure 7. Equipment debugging Let the time delay parameter l be 2. Construct the PCA model with data obtained from the normal main bearing by the DSPCA method. Hence, the monitoring effect of the model on the normal and failed bearing which is shown in the Figure 8 and Figure 9 is obtained. (1) Distribution of of the failed main bearing on the shield machine (1) Distribution of for the normal main bearing on the shield machine (2) Distribution of of the failed main bearing on the shield machine Figure 9 (1,2). PCA monitoring effect of the failed main bearing on the shield machine (2) Distribution of for the normal main bearing on the shield machine Figure 8 (1,2). PCA monitoring effect of the normal main bearing on the shield machine 135

5 CONCLUSION In this paper, the principal component analysis is applied to the fault diagnosis of the bearings. According to the time-varying and dynamic features of the bearing operation, the traditional principal component analysis algorithm is improved and the DSPCA algorithm is proposed, which provides a new idea and method for the processing of the bearing vibration signal. The the conventional signal processing method is shown as follows. Before the analysis of the signal, the original data is filtered until the purpose of filtering noise interference is achieved. However, this kind of signal is filtered as the interference signal when the conventional signal processing method is applied due to the low main bearing vibration frequency of the shield. Therefore, this paper construct the PCA monitoring model by the first section method. Indexes sensitive to the bearing state are taken as input variables of the model, so the monitored object is more pertinent and the change of bearing state is easier to be observed. 6 ACKNOWLEDGEMENTS National Natural Science Foundation of China Youth Project (No. 51405345) 7 REFERENCES Fadda, M.L., Moussaoui, A. (2018). Hybrid SOM PCA method for modeling bearing faults detection and diagnosis, Journal of the Brazilian Society of Mechanical Sciences and Engineering, 40(5), 1-8 Fu, Y.X, Jia, L.M, Qin, Y., Yang, J. (2017). Roller Bearing Fault Diagnosis Method Based on LMD-CM-PCA. Journal of Vibration,Measurement & Diagnosis, 37(2), 249-255+400 Gu, Y.K., Cheng, Z.X., Zhu, F.L. (2016). Rolling Bearing Fault Feature Fusion Based on PCA and SVM, China Mechanical Engineering, 10(20), 2778-2783 He, Z.J., Chen, J., Wang, T.Y., Zhu, F.L. (2010). Theory and application of mechanical fault diagnosis. Beijing: Higher Education Press, 6, 33-36 Jeng, J.C. (2010). Adaptive process monitoring using efficient recursive PCA and moving window PCA algorithms, Journal of the Taiwan Institute of Chemical Engineers, 41(4), 475-481. Li, Z.N, Wang, X.Y., Zhang, X.G. (2008). A rolling bearing fault pattern recognition method based on kernel principal component analysis, bearing, 06, 36-39 Liu, Y.B. (2011). Nonlinear signal analysis for rolling bearing condition monitoring and fault diagnosis. A dissertation for doctor`s degree: university of science and technology of china. Liu, X.Q., Kruger,U., Littler, T., Xie, L., Wang, S.Q. (2009). Moving window kernel PCA for adaptive monitoring of nonlinear processes, Chemometrics and Intelligent Laboratory Systems, 96(2), 132-123 Mei, H.B. (1996). Theory, method and system for the vibration monitoring and diagnosis of rolling bearing, Beijing: Mechanical Industry Press. Mi, K., Hu, Y. (2013). Bearing Condition Recognition Based on Kernel Principal Component Analysis and Genetic Programming, Applied Mechanics and Materials,08(397), 189-192 Mohanty, S., Gupta, K.K., Raju, K.S. (2017). Adaptive fault identification of bearing using empirical mode decomposition-principal component analysis-based average kurtosis technique, IET Science, Measurement and Technology, 11(1), 30-40. Ou, L., Yu, D.J. (2014). Rolling Bearing Fault Diagnosis Based on Supervised Laplaian Score and Principal Component Analysis. Journal of Mechanical Engineering,5(50), 88-94 Widodo,A., Kim,E.Y., Son,J.D., Yang, B.S., Tan, A.C.C., Gu, D.S., Choi, B.K., Mathew, J.(2009). Fault diagnosis of low speed bearing based on relevance vector machine and support vector machine, Expert systems with applications,36(3), 7252-7261 Wu, J., Wu, C.Y., Lv, Y.Q.,Deng, C., Shao, X.Y. (2017). Design a degradation condition monitoring system scheme for rolling bearing using EMD and PCA, Industrial Management and Data Systems, 117(4), 713-728. Xu, Z.F., Zhang, H.Y., Wang, D., Zhang, M.L. (2014). Study on Feature Extraction and Diagnosis Method of Rolling Bearing Faults Based on EMD and KPCA, Mechanical Science and Technology for Aerospace Engineering, 10(33), 1518-1527 Yan,W.W.,Zhang,C.K.,Shao,H.H. (2005). Nonlinear fault diagnosis method based on kernel principal component analysis.high Technology Letters(English Language Edition),5, 189-192. Zhang, L.F., Zhang, C.L., Ji, J.J. (2018). Approach for bearing fault diagnosis based on KPCA and ELM, Journal of Electronic Measurement and Instrumentation, 02, 23-29 Zvokelj,M., Zupan,S., Prebil,l. (2010). Multivariate and multi-scale monitoring of largesize low speed bearings using ensemble empirical mode decomposition method combined with principal component analysis. Mechanical systems and signal processing,5, 1049-1067. 136